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Posted: Tuesday, March 29, 2016 11:59:52 AM
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Lambda calculus


Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It was first introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics. Lambda calculus is a universal model of computation equivalent to a Turing machine (Church-Turing thesis, 1937[1]). Its namesake, Greek letter lambda (λ), is used in lambda terms (also called lambda expressions) to denote binding a variable in a function.

Lambda calculus may be typed and untyped. In typed lambda calculus functions can be applied only if they are capable of accepting the given input's "type" of data.

Lambda calculus has applications in many different areas in mathematics, philosophy,[2] linguistics,[3][4] and computer science.[5] Lambda calculus has played an important role in the development of the theory of programming languages. Functional programming languages implement the lambda calculus. Lambda calculus also is a current research topic in Category theory.[6]

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